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Papessa [141]
3 years ago
7

Find z 1 z 2 if z 1 = 3(cos37° + isin37°) and z 2 = (cos53° + isin53°

Mathematics
1 answer:
Mashutka [201]3 years ago
5 0

Answer:

Z_{1} Z_{2}  = 3 i

Step-by-step explanation:

<u>Step(i)</u>:-

Given z 1 = 3(cos 37° + i sin 37°)

          z 2 = (cos 53° + i sin 53°)

by using complex numbers

      Z_{1} = r_{1} ( cos\alpha_{1}  + isin\alpha_{1}  ) = r_{1} cis\alpha _{1}

      Z_{2} = r_{2} ( cos\alpha_{2}  + isin\alpha_{2}  ) = r_{2} cis\alpha _{2}

<u><em>step(ii)</em></u>:-

now

   Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})

       z ₁ = 3(cos 37° + i sin 37°) = 3 c i s 37°

       z ₂ = (cos 53° + i sin 53°) = c i s 53°

we will use formula

     Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})

     Z_{1} Z_{2} = 3 X 1 cis (37 + 53) = 3cis (90) = 3 cis(\frac{\pi }{2} )

    Z_{1} Z_{2} = 3(cos(\frac{\pi }{2} ) + isin(\frac{\pi }{2}))

    Z_{1} Z_{2} = 3(0 + i (1)) = 3 i

<u><em> Conclusion:</em></u>-

       Z_{1} Z_{2}  = 3 i

       

 

     

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